Is there a Guide to Adding functions ?

[JonTidswell]

I was looking to add some functions to sleef.

To simplify testing, I would like to get the scalar versions working before writing simd versions.

Is there an guide to incrementally add functions to the dispatcher ?

thanks,
-- JonT

[shibatch]

Generally speaking, adding a function that meets the accuracy requirements is pretty hard.
When I add a new function to SLEEF, I first implement it as a scalar function, and test its accuracy with a small program independent of SLEEF.

If you are planning to upstream your function, I would like to see the scalar implementation first.

[JonTidswell]

I am only targeting faithful not correct rounding, because well ... the table makers dilemma. 😉

Some coefficients I found using a linear program, and the remainder I used sollya's fpminimax to derive them.

Then I've built some Julia workbooks to try to show that using fma and with key pieces in double-double that

1. the floating point implementations are under 0.5 ulps so that I can be confident that they are under 1 ulp after final rounding. (in excess of $10^8$ samples under 0.4 ulps is not a proof, but its a start)
2. the strength reduction and reconstruction holds on the input domains on which I am interested.

Notes:

1. At this stage I'm planning to inline some simpler functions to exploit pipeline parallelism, but I should make use of whole function inlining [Add generators of headers for inlining whole sleef functions #282] rather than do it manually.
2. I know that depending on the definition of ulp that 1 ulp is not necessarily equivalent to faithful rounding at binade boundaries, so I will have to check them explicitly. (Not done yet.)

Since I was hoping to publish the key pieces, I'd rather not discuss the function specifics in an open forum.

thanks,
-- JonT

[shibatch]

Sounds good, but how can I help you?

[JonTidswell]

Mmmm.
It is more than 4.
Was this generated with Horner or changes to Estrin ? (I renamed them to u5 with Estrin because I found examples over 4 with Estrin in single precision, and too close to 4 in double precision to believe that they would stay under. )

[JonTidswell]

Its Horner, and this example goes away with Estrin.

[shibatch]

Could you use POLY21 macro, which is defined in src/common/estrin.h?
The last few terms should be evaluated with Horner.
In other functions, the last few terms are evaluated in DD precision to make the resulting accuracy under 1ulp.

[JonTidswell]

Probably, but I start to run into the problem that this thread is about - how to properly integrate and test functions in sleef.
( Without the macro I can test easily enough in Julia. :)

[ For reference I think a test value of 0.14 has a 2 ulp error when the polynomial is evaluated in mpfr. ]

Wolfram: erfinv( 0.14000000000000001332267629550187848508358001708984375 )

• 0.12471536794266059546900356708549725509490189605721092

xerfinv ( 0.14 ) evauluated using arbitrary precision

• 0.12471536794266056692663257298785432210775298235778314031618117312126

Error is ~ 2.7755575615628914e-17
ulp is ~ 1.3877787807814457e-17

[shibatch]

At this point, I use a simple program separate from sleef to check the accuracy, but you can carry out continuous testing with tester2.